The range of $f(x) = \sec \left( \frac{\pi }{4} \cos^2 x \right)$ for $-\infty < x < \infty$ is

The domain of the real valued function $f(x) = \sqrt{9 - \sqrt{x^2 - 144}}$ is

The domain of the real-valued function $f(x) = \frac{\sqrt{|x|-x}}{\sqrt{x-[x]}}$ is

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $x$).

Let $D$ be the domain of the function $f(x) = \sin^{-1} \left(\log_{3x} \left(\frac{6+2 \log_3 x}{-5x}\right)\right)$. If the range of the function $g: D \rightarrow R$ defined by $g(x) = x - [x]$ (where $[x]$ is the greatest integer function) is $(\alpha, \beta)$,then $\alpha^2 + \frac{5}{\beta}$ is equal to

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection, then $B$ is equal to